Tony Abbott has backed away from a call for the Northern Territory government to reinstate a banned drinkers' register amid concerns at an increase in alcohol-fuelled violence in indigenous communities.

After calling for the register to be ''preserved'' in a speech to Parliament on Wednesday, the Opposition Leader has bowed to a defiant refusal by the territory's new Country Liberal Party government to reinstate it.

While he said he shared the Prime Minister's concerns about watering down alcohol restrictions in the territory, Mr Abbott told reporters on Thursday he was ''not in the business of being dictatorial or prescriptive''.

Indigenous Affairs Minister Jenny Macklin said the about-face was extremely disappointing. ''One call from his Country Liberal mates and it seems Tony Abbott is no longer ready to do what's necessary to tackle alcohol abuse,'' she said.

Acting NT Chief Minister Robyn Lambley on Wednesday rejected calls to reinstate the register, saying police statistics showed that it did not work to reduce alcohol-related violence.

This was at odds with Ms Macklin's assertion that dismantling the register had contributed to increased alcohol-related assaults and hospital admissions. NT police declined to clarify this issue.

Mr Abbott said he would be happy to hear from the territory about more effective measures than the register, insisting he was not interested in ''argy-bargy'' between governments.

''What I'm interested in is getting a better outcome on the ground and what we need is to clean up the terrible epidemic of problem drinking that we've seen in so many parts of the territory and other parts of remote Australia,'' he said.